非光滑多目标分式鲁棒优化问题的最优性条件与Mond-Weir型对偶
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国家自然科学基金地区科学基金项目(No.11961072);陕西省教育厅科学研究计划项目(No.17JK0860)


Optimality Conditions and Mond-Weir Type Duality for Nonsmooth Multiobjective Fractional Robust Optimization Programming
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    摘要:

    研究了非光滑多目标分式鲁棒优化问题,借助Gordan择一定理和极大极小定理在非光滑的Extended Mangasarian-Fromovitz约束下建立了最优性必要条件;接着引入广义凸-凹函数,给出Mond-Weir型对偶模型,在广义凸性的假设下得到对偶问题与原问题的强、弱对偶和逆对偶定理。研究结果丰富了优化理论的研究内容,并为求解多目标优化问题提供了新的算法依据。

    Abstract:

    The nonsmooth multiobjective fractional robust optimization problem is investigated. By employing the Gordan alternative theorem and minimax theorem, necessary optimality conditions are established under nonsmooth Extended Mangasarian-Fromovitz constraint qualifications. Subsequently, generalized convex-concave functions are introduced. A Mond-Weir type dual model is then proposed. Under generalized convexity assumptions, strong duality, weak duality, and converse duality theorems between the dual problem and the original problem are derived. These results enrich the theoretical framework of optimization theory and provide new algorithmic foundations for solving multiobjective optimization problems.

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吴浩,李向有.非光滑多目标分式鲁棒优化问题的最优性条件与Mond-Weir型对偶[J].重庆师范大学学报自然科学版,2025,42(2):59-67

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  • 在线发布日期: 2025-06-06